Assume that the company that you selected for the Module 1 SLP has a bond outstanding that
matures in 20 years and has a coupon rate of 6.5%. The par value of the bond is $1,000.
If the yield to maturity is 8% and the bond pays interest on an annual basis, what’s the current
price of the bond? Is the bond selling for a premium or discount? How can you tell?
If the yield to maturity is 8% but the bond pays interest on a semi-annual basis instead of an
annual basis, what’s the current price of the bond? Is it different from the value when using
annual compounding? Explain.
Now, assume that the economy enters into a recession and interest rates fall. The bond’s yield
to maturity is now 5%. What’s the bond’s new price? How does the price compare with your
answer in part a? Why did the bond’s value change?
A bond matures in ten years and is currently selling for $1,125. The bond pay interest annually,
has a par value of $1,000, and a yield to maturity of 10.75%. What’s the bond’s current yield?
Write a 2-page essay comparing reinvestment risk and interest rate risk and how an investor
can protect his or her portfolio from those risks.
FIN501SLP 2 2
Calculation of bond prices stem from the formular yield = Coupon Amount divide by the price.
When bond is sold at its original price that’s at par, the yield is always equal to the rate of
interest charged. When the bond’s price changes it also affects the yield but inversely i.e. the
price of bonds is inversely proportional to the yield expected (Ross, Westerfield and Bradford,
The par value of the bond is 1000 and the coupon rate is 6.5%
The initial price of the bond is 6.5% X $1000 = $65
The current price of the bond is 8% * x = $65
= 65 X 100/8 = $812.5
The bond is selling at a discount. The par value of the bond was $1000 but now its $812.5. As an
investor i would be very happy to buy the bonds at a discount however, if am the holder of the
bonds I would be disappointed as I would not be able to recover the amounts I used to purchase
the bonds. I purchased them at $1000 each but now there prices have gone down to $812.5 each.
b. If the yield to maturity is 8% which is payable semi-annually then the current price of the
bond is equal to; i = 4 (two payments of 4% each semiannually) payments = 1000 and n = 2
We apply the following formula to calculate the Future value or the compound yield,
FV annuity ordinary = C * [(1+I) ^n-1/i](1+i) Where C = Payment, I = interest and n = number of years or periods of payments. where C = 10000.065 = 65/2 = 17.5, I = 4% and n = 2
Using excel calculations = 35.5 The total proceeds after the two payments periods or the
semiannual payments = 1000 + 35.5. = 1035.5 The current price of the bond = 1035
YMT = = 4% semiannually or 8% annually
Yes the value is different when using the annual compounding. The semiannual compounding
produces twice the amount of interest than the annual calculations.
The par value of the bond is 1000 and the coupon rate is 10.75%
The initial price of the bond is 10.75% X $1000 = $107.5
The current price of the bond is 8% * x = $107.5
1125/107.5 = 10.46
YTM = 10.46
Reinvestments risks are basically the risks of investors investing at lower rates of returns hence
achieving reduced rates of income than the amount invested at the investment time frame
expected. Interest rates risks are mostly occasioned by inflation risks which lead to loss in
FIN501SLP 2 4
To protect the company or investments from interest rates risks, an investor can invest in bonds.
This is one way of diversification and which can protect the value of investments. The
performance of bonds mostly does not fluctuate with the stock market hence it’s a suitable
strategy or alternative when the stock market presents uncertainties. Bonds also have the
potential of earning more income than the money market from mutual funds.
Bond prices mostly tend to drop or decrease when the interest rates are rising and to increase
when the interest is decreasing. This inverse relationship that exists between the bonds and
interest rates is what is commonly known as the interest rates risks. The interest rates risks tend
to increase when the maturity period of bonds are longer (Moyer, Kretlow, McGuigan, 2011).
Balancing the portfolio with different classes of investments can reduce the exposure to different
types of risks. For example, investing in short term treasury bills or other fixed income securities
with short duration provide effective protection to capital risks but critically increase the risks to
reinvestments risks or even inflation risk. But the risks also depend on actual duration of the
investments or securities, the economic environment, the market and the prevailing interest rates.
On the other hand the stocks provide increased protection to the risks of inflation and to some
degree reduced exposure to reinvestments risks but it increases the capital risks (Markowitz,
The risk management within a portfolio mostly focuses on the general importance of reducing
the risks or protection against each set of risks, i.e. short-term and long term treasury bills and
bonds (Burghardt, Belton, Lane and Papa, 2005).
Capital risks Inflation risks Reinvestments
Bonds Treasury Bills Stocks
Stocks Bonds Treasury
The table above shows the different methods of diversifying risks in portfolio management.
To conclude, the current or the existing interest rate environment, economic environment and the
stock market are all key determinants when selecting the appropriate portfolio asset allocation.
Mostly portfolios are designed generally to meet the needs and expectations of the investors in
protecting the long term and short term classes of investments against the exposure to
reinvestment rate risks and other risks that may affect the investments. The interest rates risks
can be controlled by investments in bonds and other short term investments.
FIN501SLP 2 6
Burghardt, G., Belton, T., Lane, M. and Papa, J. (2005) The Treasury Bond Basis. New York,
Luenberger, D. (1997). Investment Science, Oxford University Press.
Markowitz, H.M., (1991) Portfolio Selection, second edition, Blackwell.
Moyer, C., Kretlow, W., McGuigan, J. (2011). Contemporary Financial Management (12 ed.)
Winsted: South-Western Publishing Co. pp. 147–498
Ross, S., Westerfield, R.W. and Bradford, D.J. (2010). Fundamentals of Corporate Finance (9
ed.) New York: McGraw-Hill. pp. 145–287